Robert S. Parker

A model-based algorithm for blood glucose control in Type I diabetic patients

A model-based-predictive control algorithm is developed to maintain normoglycemia in the Type I diabetic patient using a closed-loop insulin infusion pump. Utilizing compartmental modeling techniques, a fundamental model of the diabetic patient is constructed. The resulting nineteenth-order nonlinear pharmacokinetic-pharmacodynamic representation is used in controller synthesis. Linear identification of an input-output model from noisy patient data is performed by filtering the impulse-response coefficients via projection onto the Laguerre basis. A linear model predictive controller is developed using the identified step response model. Controller performance for unmeasured disturbance rejection (50 g oral glucose tolerance test) is examined. Glucose setpoint tracking performance is improved by designing a second controller which substitutes a more detailed internal model including state-estimation and a Kalman filter for the input-output representation The state-estimating controller maintains glucose within 15 mg/dl of the setpoint in the presence of measurement noise. Under noise-free conditions, the model based predictive controller using state estimation outperforms an internal model controller from literature (49.4% reduction in undershoot and 45.7% reduction in settling time). These results demonstrate the potential use of predictive algorithms for blood glucose control in an insulin infusion pump.

Control-relevant modeling in drug delivery

The development of control-relevant models for a variety of biomedical engineering drug delivery problems is reviewed in this paper. A summary of each control problem is followed by a review of relevant patient models from literature, an examination of the control approaches taken to solve the problem, and a discussion of the control-relevance of the models used in each case. The areas examined are regulating the depth of anesthesia, blood pressure control, optimal cancer chemotherapy, regulation of cardiac assist devices, and insulin delivery to diabetic patients.

Dynamic Modeling of Exercise Effects on Plasma Glucose and Insulin Levels

Background: Regulation of plasma glucose concentration for type 1 diabetic patients is challenging, and exercise is an added complication. From a metabolic prospective, the significant exercise-induced effects are increased glucose uptake rate by the working tissues, increased hepatic glucose release to maintain overall glucose homeostasis, and decreased plasma insulin concentration. During prolonged exercise, glucose levels drop significantly because of the decrease in hepatic glucose production. With the long-term goal of developing a closed-loop insulin delivery system operating under various physiological conditions, it is necessary to develop a model that is capable of predicting blood glucose concentration at rest and during physical activity. Methods: A minimal model developed previously was extended to include the major effects of exercise on plasma glucose and insulin levels. Differential equations were developed to capture the exercise-induced dynamics of plasma insulin clearance and the elevation of glucose uptake and hepatic glucose production rates. The decreasing liver glucose output resulting from prolonged exercise was modeled using an equation depending on exercise intensity and duration. Results: The exercise model successfully captured the glucose and insulin dynamics during short- and long-term exercise. Model predictions of glucose and insulin dynamics during the postexercise recovery period were also consistent with literature data. Conclusion: The model successfully emulated the physiological effects of exercise on blood glucose and insulin levels. This extended model may provide a new disturbance test platform for the development of closed-loop glucose control algorithms.

The identification of nonlinear models for process control using tailored “plant-friendly” input sequences

Abstract This paper considers certain practical aspects of the identification of nonlinear empirical models for chemical process dynamics. The primary focus is the identification of second-order Volterra models using input sequences that offer the following three advantages: (1) they are “plant friendly;” (2) they simplify the required computations; (3) they can emphasize certain model parameters over others. To provide a quantitative basis for discussing the first of these advantages, this paper defines a friendliness index f that relates to the number of changes that occur in the sequence. For convenience, this paper also considers an additional nonlinear model structure: the Volterra–Laguerre model. To illustrate the practical utility of the input sequences considered here, second-order Volterra and Volterra–Laguerre models are developed that approximate the dynamics of a first-principles model of methyl methacrylate polymerization.

Model predictive control for infusion pump insulin delivery

The authors present an algorithm for controlling blood glucose in the Type I diabetic patient using model predictive control (MPG) of a closed-loop insulin infusion pump. The controller is designed from a detailed 19th order model of the human glucose-insulin system. Input constraints, based on insulin pump and physiological requirements, are enforced. The controller is challenged with a hyperglycemic diabetic patient (setpoint tracking), and a controlled diabetic ingesting a meal (unmeasured disturbance rejection). To improve both robustness and performance, a new controller using MPC with state estimation is synthesized. Compared to the non-state estimating controller, the new controller results in a 40% improvement in overshoot, to a maximum hypoglycemic deviation of 7.9 mg/dl, and a 23% decrease in settling time. These results demonstrate the potential use for this algorithm in a closed-loop insulin infusion pump.

An ensemble of models of the acute inflammatory response to bacterial lipopolysaccharide in rats : Results from parameter space reduction

In previous work, we developed an 8-state nonlinear dynamic model of the acute inflammatory response, including activated phagocytic cells, pro- and anti-inflammatory cytokines, and tissue damage, and calibrated it to data on cytokines from endotoxemic rats. In the interest of parsimony, the present work employed parametric sensitivity and local identifiability analysis to establish a core set of parameters predominantly responsible for variability in model solutions. Parameter optimization, facilitated by varying only those parameters belonging to this core set, was used to identify an ensemble of parameter vectors, each representing an acceptable local optimum in terms of fit to experimental data. Individual models within this ensemble, characterized by their different parameter values, showed similar cytokine but diverse tissue damage behavior. A cluster analysis of the ensemble of models showed the existence of a continuum of acceptable models, characterized by compensatory mechanisms and parameter changes. We calculated the direct correlations between the core set of model parameters and identified three mechanisms responsible for the conversion of the diverse damage time courses to similar cytokine behavior in these models. Given that tissue damage level could be an indicator of the likelihood of mortality, our findings suggest that similar cytokine dynamics could be associated with very different mortality outcomes, depending on the balance of certain inflammatory elements.

Clinically relevant cancer chemotherapy dose scheduling via mixed-integer optimization

Cancer is a class of diseases characterized by an imbalance between cell proliferation and programmed cell death. Chemotherapy is commonly employed as a treatment by clinicians, who must deliver the agent on a schedule that balances treatment efficacy with the toxic side effects. Engineers have considered the development of drug administration schedules for simulated cancer patients constrained by pharmacokinetic (PK) and pharmacodynamic (PD) models. The results typically involve mathematically elegant solutions, although the clinical utility of such results is limited by the formulation of the problem as well as the level of abstraction. At issue is the common disconnect between solutions that are mathematically vs. clinically optimal. The focus of this work is to develop a methodology which can explicitly account for the constraints clinicians consider implicitly. To demonstrate the clinical relevance of this methodology two case studies were considered: a theoretical system from the literature and a preclinical mouse model. The problem formulation is accomplished in a mixed-integer programming framework that is capable of solving problems with complex objectives and constraints yielding results that are clinically relevant.

Advanced model predictive control (MPC) for type I diabetic patient blood glucose control

Advanced control strategies for delivering insulin to type I diabetic patients are developed. Utilizing the model predictive control (MPC) framework, an asymmetric objective function is tailored to address the inherent performance requirements of the physiological problem. This technique is then compared to an MPC controller incorporating prioritized objectives. In an in-patient setting, a second manipulated variable (glucose infusion) could be made available. This multiple-input single-output (MISO) problem is reformulated as a multiple-input multiple-output (MIMO) output regulator problem and is solved using the above techniques. Performance in all cases was demonstrably superior to previous results based on standard MPC formulations using symmetric objective functions.

A potential role of distinctively delayed blood clearance of recombinant adeno-associated virus serotype 9 in robust cardiac transduction.

Recombinant adeno-associated virus serotype 9 (rAAV9) vectors show robust in vivo transduction by a systemic approach. It has been proposed that rAAV9 has enhanced ability to cross the vascular endothelial barriers. However, the scientific basis of systemic administration of rAAV9 and its transduction mechanisms have not been fully established. Here, we show indirect evidence suggesting that capillary walls still remain as a significant barrier to rAAV9 in cardiac transduction but not so in hepatic transduction in mice, and the distinctively delayed blood clearance of rAAV9 plays an important role in overcoming this barrier, contributing to robust cardiac transduction. We find that transvascular transport of rAAV9 in the heart is a capacity-limited slow process and occurs in the absence of caveolin-1, the major component of caveolae that mediate endothelial transcytosis. In addition, a reverse genetic study identifies the outer region of the icosahedral threefold capsid protrusions as a potential culprit for rAAV9s delayed blood clearance. These results support a model in which the delayed blood clearance of rAAV9 sustains the capacity-limited slow transvascular vector transport and plays a role in mediating robust cardiac transduction, and provide important implications in AAV capsid engineering to create new rAAV variants with more desirable properties.

Ensemble models of neutrophil trafficking in severe sepsis.

A hallmark of severe sepsis is systemic inflammation which activates leukocytes and can result in their misdirection. This leads to both impaired migration to the locus of infection and increased infiltration into healthy tissues. In order to better understand the pathophysiologic mechanisms involved, we developed a coarse-grained phenomenological model of the acute inflammatory response in CLP (cecal ligation and puncture)-induced sepsis in rats. This model incorporates distinct neutrophil kinetic responses to the inflammatory stimulus and the dynamic interactions between components of a compartmentalized inflammatory response. Ensembles of model parameter sets consistent with experimental observations were statistically generated using a Markov-Chain Monte Carlo sampling. Prediction uncertainty in the model states was quantified over the resulting ensemble parameter sets. Forward simulation of the parameter ensembles successfully captured experimental features and predicted that systemically activated circulating neutrophils display impaired migration to the tissue and neutrophil sequestration in the lung, consequently contributing to tissue damage and mortality. Principal component and multiple regression analyses of the parameter ensembles estimated from survivor and non-survivor cohorts provide insight into pathologic mechanisms dictating outcome in sepsis. Furthermore, the model was extended to incorporate hypothetical mechanisms by which immune modulation using extracorporeal blood purification results in improved outcome in septic rats. Simulations identified a sub-population (about of the treated population) that benefited from blood purification. Survivors displayed enhanced neutrophil migration to tissue and reduced sequestration of lung neutrophils, contributing to improved outcome. The model ensemble presented herein provides a platform for generating and testing hypotheses in silico, as well as motivating further experimental studies to advance understanding of the complex biological response to severe infection, a problem of growing magnitude in humans.